{"id":"aqua_rat:95703b14065976c1b7b25822fcf7dc4f","source_id":"aqua_rat","source_item_id":"95703b14065976c1b7b25822fcf7dc4f","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"A man spend 810 in buying trouser at Rs 70 each and shirt at 30 each. What will be the ratio of trouser and shirt when the maximum number of trouser is purchased?","stimulus":"","stimulus_html":null,"stem_html":"<p>A man spend 810 in buying trouser at Rs 70 each and shirt at 30 each. What will be the ratio of trouser and shirt when the maximum number of trouser is purchased?</p>","rationale_html":"<p>Lets assume S as price of shirt and T as price of trousers, we have bellow equation:</p><p>70 T + 30 S = 810</p><p>Simplifying we get : 7T + 3S = 81</p><p>T = ( 81 - 3*S )/7</p><p>We need to find the least value of S which will make (81 - 3*S) divisible by 7</p><p>Simplifying by taking 3 as common factor 3*(27-S) / 7</p><p>Looking at the above equation its not difficult to find out least value of S is 6 so that 27- 3S becomes divisible by S</p><p>Hence, T = (81-3*S)/7 = (81-3*6)/7 = 63/7 = 9</p><p>A</p>","correct_answer":["A"],"equiv_key":"b503cdf670d14c783a49efc7","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>9 Trousers</p>","ord":0},{"label":"B","content_html":"<p>8 Trousers</p>","ord":1},{"label":"C","content_html":"<p>10 Trousers</p>","ord":2},{"label":"D","content_html":"<p>7 Trousers</p>","ord":3},{"label":"E","content_html":"<p>11 Trousers</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}